A batter hits a home run, the ball leaves the field of play. The batter does not tag home plate in a celebration. The umpire gives the catcher a new ball. The batter goes back to touch home plate but the catcher tags the batter and the umpire calls the batter out. Run does not count. Is the batter out or safe?

I find the question ambiguous. How far was the runner that he had to "go back" to the plate? Was it two steps and turned around? Was it down to the dugout when someone pushes him back onto the field? 5.09(b)(2) is possible.
– BowlOfRedMay 6 '17 at 0:05

1 Answer
1

(4) He fails to touch home base and makes no attempt to
return to that base, and home base is tagged.

I would also cite rule 5.02 on page 34, which says (emphasis added):

5.02 After the umpire calls “Play” the ball is alive and in play and remains alive and in play until for legal cause, or at the umpire’s call of “Time” suspending play, the ball becomes dead. While the ball is dead no player may be put out, no bases may be run and no runs may be scored, except that runners may advance one or more bases as the result of acts which occurred while the ball was alive (such as, but not limited to a balk, an overthrow, interference, or a home run or other fair ball hit out of the playing field).

and rule 5.12 about dead balls, which states:

After the ball is dead, play shall be resumed when the pitcher takes his place on the pitcher’s plate with a new ball or the same ball in his possession and the plate umpire calls “Play.” The plate umpire shall call “Play” as soon as the pitcher takes his place on his plate with the ball in his possession.

In this case, the ball was dead (by virtue of being a homerun). From Rule 5.02, no player may be put out while the ball is dead. According to rule 5.12, the ball is not "Live" yet, since the pitcher had not taken his place on the plate with a new ball and the umpire didn't say "Play". The batter was trying to return to the base while the ball was still dead. So I'd conclude that the requirements for 4.09(c)(4) were not met and the player should have been safe.